Orbital Ordering in Charge Transfer Insulators

We discuss a new mechanism of orbital ordering, which in charge transfer insulators is more important than the usual exchange interactions and which can make the very type of the ground state of a charge transfer insulator, i.e., its orbital and magnetic ordering, different from that of a Mott-Hubbard insulator. This purely electronic mechanism allows us to explain why orbitals in Jahn-Teller materials typically order at higher temperatures than spins, and to understand the type of orbital ordering in a number of materials, e.g., ${\mathrm{K}}_2{\mathrm{CuF}}_4$, without invoking the electron-lattice interaction.

Figure 1

Diagrams describing interactions mediated by two virtual oxygen holes.

Figure 2

Favorable [(a) and (b)] and unfavorable (c) occupations of hole orbitals of neighboring TM ions in CTI, in which the exchange is dominated by Eq. (4).

Figure 3

The orbital ground state and the total spin $S$ of a pair of JT ions with one hole/electron per site in MHI, CTI, and materials with the strong JT interaction.